Express your answer as a mixed number simplified to lowest terms. $10\dfrac{2}{14}-6\dfrac{1}{3} = {?}$
Solution: Simplify each fraction. $= {10\dfrac{1}{7}} - {6\dfrac{1}{3}}$ Find a common denominator for the fractions: $= {10\dfrac{3}{21}}-{6\dfrac{7}{21}}$ Convert ${10\dfrac{3}{21}}$ to ${9 + \dfrac{21}{21} + \dfrac{3}{21}}$ So the problem becomes: ${9\dfrac{24}{21}}-{6\dfrac{7}{21}}$ Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{24}{21}} - {6} - {\dfrac{7}{21}}$ Bring the whole numbers together and the fractions together: $= {9} - {6} + {\dfrac{24}{21}} - {\dfrac{7}{21}}$ Subtract the whole numbers: $=3 + {\dfrac{24}{21}} - {\dfrac{7}{21}}$ Subtract the fractions: $= 3+\dfrac{17}{21}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{17}{21}$